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TI-84 Calculator for Calculus

Master calculus with your TI-84 calculator. Compute derivatives, integrals, and limits with precision. Perfect for AP Calculus, college calculus courses, and advanced mathematical analysis.

Complete Calculus Toolkit

Everything you need to excel in differential and integral calculus

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Derivative Calculator

Calculate derivatives numerically and graphically. Find slopes at specific points, analyze rates of change, and explore the relationship between functions and their derivatives.

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Integral Calculator

Compute definite integrals numerically with high precision. Find areas under curves, solve accumulation problems, and verify antiderivative calculations.

Explore Integration β†’
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Function Analysis

Analyze function behavior including critical points, inflection points, concavity, and extrema. Visualize functions and their first and second derivatives.

Analyze Functions β†’
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Limit Investigation

Investigate limits graphically and numerically. Explore continuity, one-sided limits, and limits at infinity using tables and graphs.

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Optimization Problems

Solve real-world optimization problems by finding maximum and minimum values. Use calculus tools to solve practical applications in business, physics, and engineering.

Optimize Solutions β†’
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Series & Sequences

Work with infinite series, Taylor polynomials, and sequence convergence. Explore power series and their applications in approximating functions.

Explore Series β†’

See Calculus in Action

Watch how the TI-84 solves common calculus problems

Finding a Derivative
Y1 = X^3 - 2*X^2 + 1
f'(2) = nDeriv(Y1,X,2)
8
Graph β†’ CALC β†’ dy/dx
At X=2: dy/dx=8
πŸ“Š Try Derivatives
Computing an Integral
Y1 = X^2
βˆ«β‚€Β² XΒ² dx = fnInt(Y1,X,0,2)
2.66666667
Graph β†’ CALC β†’ ∫f(x)dx
∫f(x)dx = 8/3
∫ Try Integration
Finding Maximum/Minimum
Y1 = -X^2 + 4*X - 1
Graph Function
CALC β†’ Maximum
Maximum: (2, 3)
Vertex of parabola
🎯 Find Extrema

Common Calculus Problems

Step-by-step solutions to typical calculus problems

Related Rates Problem

Problem: A balloon is being inflated so that its volume increases at 100 cmΒ³/min. How fast is the radius changing when r = 5 cm?

TI-84 Approach:
β€’ V = (4/3)Ο€rΒ³
β€’ dV/dt = 4Ο€rΒ² Γ— dr/dt
β€’ 100 = 4Ο€(5)Β² Γ— dr/dt
β€’ Solve: dr/dt = 100/(100Ο€)
βœ“ Answer: dr/dt β‰ˆ 0.318 cm/min

Area Between Curves

Problem: Find the area between y = xΒ² and y = 4 - xΒ²

TI-84 Method:
β€’ Find intersection: xΒ² = 4 - xΒ²
β€’ Solve: x = ±√2
β€’ Set up: βˆ«β‚‹βˆšβ‚‚^βˆšβ‚‚ (4 - xΒ² - xΒ²) dx
β€’ Calculate: fnInt(4-2*X^2,X,-√(2),√(2))
βœ“ Answer: 32√2/3 β‰ˆ 15.09 square units

Optimization - Maximum Volume

Problem: A box is made from 24Γ—24 inch cardboard by cutting equal squares from corners. Find dimensions for maximum volume.

Solution Steps:
β€’ V(x) = x(24-2x)Β²
β€’ Graph Y1 = X*(24-2*X)^2
β€’ Use CALC β†’ Maximum
β€’ Find critical point
βœ“ Answer: Cut 4Γ—4 inch squares

Implicit Differentiation

Problem: Find dy/dx for xΒ² + yΒ² = 25 at point (3,4)

TI-84 Verification:
β€’ Solve: y = √(25-xΒ²)
β€’ Y1 = √(25-XΒ²)
β€’ Find slope: nDeriv(Y1,X,3)
β€’ Verify: -x/y = -3/4
βœ“ Answer: dy/dx = -3/4

Limits Using L'HΓ΄pital's Rule

Problem: lim(x→0) (sin x)/x

TI-84 Investigation:
β€’ Y1 = sin(X)/X
β€’ Use TABLE with values near 0
β€’ X: -0.1, -0.01, 0.01, 0.1
β€’ Observe Y1 values approaching 1
βœ“ Answer: Limit = 1

Taylor Series Approximation

Problem: Approximate e^x using Taylor series at x = 0

TI-84 Comparison:
β€’ Y1 = e^(X) (actual function)
β€’ Y2 = 1 + X + XΒ²/2 + XΒ³/6 (degree 3)
β€’ Y3 = Y2 + X⁴/24 + X⁡/120 (degree 5)
β€’ Compare graphs and values
βœ“ Higher degree = better approximation

Master Calculus Today

Start solving calculus problems with confidence. Our free TI-84 calculator and comprehensive guides will help you excel in differential and integral calculus.

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